Integrating JIRA with external application

I am able to make requests to JIRA rest api using basic authentication and OAUTH.

Basic Authentication is not correct for my requirement because the requests must be made in the name of the currently logged-in users from the external application. Where as OAuth is user specific token and here problem is work log logged under the user who generated the token but wanted to log as logged-in user of the external application.

currently my JIRA is having "resolution SAML" plugin.

I am very new to the SSO concept, can any one guide how can I make requests to the JIRA application with the logged-in user info. And my external application doesn't have any Active directory.

Finally my expectation is make JIRA REST api calls but not with Basic Authentication and OAuth, is there way to make requests to JIRA REST calls.